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Posterior Sensitivity to the Sampling Distribution and the Prior: More than One Observation
Authors:Sanjib Basu
Institution:(1) Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, 72701, U.S.A.
Abstract:Sensitivity of a posterior quantity rgr(f, P) to the choice of the sampling distribution f and prior P is considered. Sensitivity is measured by the range of rgr(f, P) when f and P vary in nonparametric classes Gamma f and Gamma P respectively. Direct and iterative methods are described which obtain the range of rgr(f, P) over fisinGamma f when prior P is fixed, and also the overall range over fisinGamma f and PisinGamma P . When multiple i.i.d. observations X 1,...,X k are observed from f, the posterior quantity rgr(f, P) is not a ratio-linear function of f. A method of steepest descent is proposed to obtain the range of rgr(f, P). Several examples illustrate applications of these methods.
Keywords:Bayesian robustness    teaux derivative  model robustness  model selection  predictive distribution  prior robustness  steepest descent
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